In the art of elevator-type material conveyor systems, containers or so-called “buckets” are supported spaced-apart on an endless belt for moving particular material substantially vertically. The ends of such elevator belts and/or the ends of two adjacently positioned elevator belts are typically secured together by belt splices, stapling or some other attaching method. However, many current methods of attachment and designs are susceptible to premature failure. For example, many elevator belt splices are unable to withstand the high tension forces acting on elevator belts during operation. Furthermore, many existing splice designs are unable to effectively support the curvature of the portion of the belt between the tension plane and the actual clamping surface of the belt. In addition, the manufacture of many current elevator belt designs results in devices that bulky and expensive to manufacture. More importantly, such designs are unable to accommodate differing sized belts (i.e., belts having different thicknesses). There remains a need for belt clamping or splice devices that overcome the problems mentioned.